Light-emitting diodes (LEDs) are widely used in various applications, including indicators, light sensors, traffic lights, broadband data transmission, and illumination applications. Particularly, LEDs attract more interest for illumination applications due to their low power consumption and long lifetime. In illumination applications, LEDs have some limitations, such as narrow band spectrum. The narrow band spectrum can be overcome by integrating various types of LEDs to provide white light. Another limitation is directional emission. The emission light power from the LEDs is usually distributed in a small solid angle, which provides a narrow viewing angle and is dissimilar to natural illumination. Such directive illumination and bright forward lighting make human eyes uncomfortable and irritate the human eyes. Unless illumination in a specific direction is required for a special application, the narrow viewing angle of LED illumination is undesired, especially in indoor illumination uses. Currently, indoor LED lamps use a Lambertian based emitter and a diffuser-based cap to distribute the emitted light. However, those techniques for light distribution can only achieve up to 140 degree illumination and has little backward light. So, the LED emission is still directive and cannot form a uniform light distribution pattern. Therefore, structures and methods of LED structures are needed to address the above issues.